Aw, Samwise! I like it ever so much, especially as a middle. I don't know if there are any Tolkien names I'd actually use as firsts, because most of them are so tied to the mythology--many of them even created for it--that it would just scream "MY PARENTS WERE TOLKIEN FANS!" all my child's life. Being a Tolkien fan is an awesome thing, but I think I'd be a little squeamish about labeling another person that distinctively. That said, most of the names would make incredible middles.

Thanks to Ottilie, I realized lately how awesome Elessar would be as a middle. Some other favorites of mine:

Maedhros (from the Silmarillion; the oldest and one of the noblest of Feanor's sons. Pronounced MY-thross, TH as in thee.)
Fingolfin (Also from the Silmarillion. A bit much as a name, I realize, but he was the Elf who, when all hope was lost, challenged the Dark Lord Morgoth to single combat. Although he was defeated, he gave Morgoth seven wounds from the pain of which Morgoth was never free again.)
Finrod (Silmarillion again)
Bregalad (The Ent who entertained Merry and Pippin during the Ent-moot. He was in charge of rowan-trees.)
Elladan and Elrohir (the twin sons of Elrond, conveniently left out of the movies I don't know if I could use one and not the other, though!)
Elrond, of course
Faramir, of course (mentioned by others, but he's one of my very favorites! What a sweet guy.)
Imrahil (Prince of Dol Amroth. He came to aid Gondor in the Battle of the Pelennor Fields. Eomer later married his daughter, Lothiriel.)

And there are a few awesome names in Merry's Brandybuck family tree, which looks Welsh-inspired:

I love the name Samwise. He is my favorite Tolkien character (and from something I read, possibly Tolkien's favorite as well). My husband and I have both talked about that as a likely future boys name. Even if the kid thought it was "weird," he could easily go by Sam. And, in my experience, Sams tend to be really likable guys.